The aim of this paper is to study the squeezing and statistical properties of the light produced by a degenerate three-level laser whose cavity contains a degenerate parametric amplifier. In this quantum optical system the top and bottom levels of the three-level atoms injected into the laser cavity are coupled by the pump mode emerging from the parametric amplifier. For a linear gain coefficient of 100 and for a cavity damping constant of 0.8, the maximum intracavity squeezing is found at steady state and at threshold to be 93%.
It is commonly accepted that a parametric amplifier can simulate a phase-preserving linear amplifier regardless of how the latter is realized [Caves et al., Phys. Rev. A 86, 063802 (2012)]. If true, this reduces all phase-preserving linear amplifiers to a single familiar model. Here we disprove this claim by constructing two counterexamples. A detailed discussion of the physics of our counterexamples is provided. It is shown that a Heisenberg-picture analysis facilitates a microscopic explanation of the physics. This also resolves a question about the nature of amplifier-added noise in degener…
We propose a new scheme for realizing nonlocal nondegenerate optical parametric amplifier by means of genuine four-mode entanglement. The nondegenerate optical parametric amplifier is regarded as a unitary transformation from two input fields to two outputs. Two inputs and two outputs are located at the remote stations respectively. Employing off-line four-mode entanglement, homodyne detection, classical communication and local displacement, the nonlocal nondegenerate optical parametric amplifier can be achieved. This scheme can be implemented with a setup that is experimentally accessible at …
A parametric amplifier is in essence a linear four-port device, which couples and linearly mixes two inputs before amplifying and sending them to two output ports. Here, we show that for quadrature-phase amplitudes, a parametric amplifier can replace beam splitters to play the role of mixer. We apply this idea to a continuous-variable quantum state teleportation scheme in which a parametric amplifier replaces a beam splitter in Bell measurement. We show that this scheme is loss-tolerant in the Bell measurement process and thus demonstrate the advantage of PA over BS in the applications in quan…
Applying stochastic differential equations, we study the squeezing and statistical properties of the cavity and output modes of a degenerate three-level laser whose cavity contains a parametric amplifier and coupled to a squeezed vacuum reservoir. We consider the case in which the top and bottom levels of the three-level cascade atoms injected into the cavity are coupled by the pump mode emerging from the parametric amplifier. It turns out that the presence of the squeezed vacuum reservoir and the parametric amplifier contribute considerably to the mean photon number and the degree of squeezin…
We study how an optical parametric amplifier inside the cavity can affect the normal mode splitting behavior of the coupled movable mirror and the cavity field. We work in the resolved sideband regime. The spectra exhibit a double-peak structure as the parametric gain is increased. Moreover, for a fixed parametric gain, the double-peak structure of the spectrum is more pronounced with increasing the input laser power. We give results for mode splitting. The widths of the split lines are sensitive to parametric gain.
We demonstrate vacuum squeezing at the D1 line of atomic rubidium (795 nm) with a tunable, doubly-resonant, monolithic sub-threshold optical parametric oscillator in periodically-poled Rb-doped potassium titanyl phosphate. The squeezing appears to be undiminished by a strong dispersive optical nonlinearity recently observed in this material.
Superconducting parametric amplifiers are crucial components in microwave quantum circuits for enabling quantum-limited signal readout. The best-performing such amplifiers are often based on Josephson junctions, which however are sensitive to magnetic fields. Therefore, they require magnetic shields and are not easily integratable with other quantum systems that operates within magnetic fields, such as spin ensemble quantum memories. To tackle this challenge, we have developed a kinetic inductance-based parametric amplifier featuring a NbN nanobridge instead of Josephson Junctions, which provi…
The process of heralded noiseless amplification, and the inverse process of heralded noiseless attenuation, have potential applications in the context of quantum communications. Although several different physical implementations of heralded noiseless amplifiers have now been demonstrated, the research on heralded noiseless attenuators has been largely confined to a beam-splitter based approach. Here we show that an optical parametric amplifier (OPA), combined with appropriate heralding, can also serve as a heralded noiseless attenuator. The counterintuitive use of an optical amplifier as an a…
A particularly simple setup is introduced to study the influence of time-delayed coherent feedback on the optical squeezing properties of the degenerate parametric amplifier (DPA). The possibility for significantly enhanced squeezing is demonstrated both on resonance and in sidebands, at a reduced pump power compared to the case without feedback. We study a broad range of operating parameters and their influence on the characteristic squeezing of the system. A classical analysis of the system dynamics reveals the connection between the feedback-modified landscape of stability and enhanced sque…
We report the experimental demonstration of polarization squeezed beam at 795 nm by combining a quadrature squeezed beam with a coherent beam. The quadrature squeezed beam is generated by a degenerate optical parametric amplifier based on a PPKTP crystal. Stokes parameter squeezing of -3.8 dB and anti squeezing of +5.0 dB is observed. This polarization squeezed beam resonant to rubidium D1 line has potential applications in quantum information networks and precise measurement beyond the shot noise limit.
Quantum illumination is a quantum-optical sensing technique in which an entangled source is exploited to improve the detection of a low-reflectivity object that is immersed in a bright thermal background. Entangled sources between microwave and optical fields can be exploited to improve detection in microwave quantum illumination technique. We proposed a scheme to enhance the entanglement between the output fields of microwave and optical cavity by introducing optical parametric amplifier medium in cavity optomechanical system. We show that improving signal-to-noise ratio and decreasing error …
Optimizing Pump Conditions of Parametric Amplifiers for Fast Multiplexed Readout of Superconducting Qubits
Quantum Machines Inc.（量子机器公司）；IQCC（以色列量子计算中心）；SKKU Advanced Institute of Nanotechnology, Sungkyunkwan University（成均馆大学SKKU纳米技术高等研究院）；Department of Quantum Information Engineering, Sungkyunkwan University（成均馆大学量子信息工程系）
By utilizing the nondegenerate optical parametric amplifier, the quantum state transfer from a pump state with high frequency to a signal state of lower frequency is studied theoretically. The noiseless state transfer is characterized by frequency conversion efficiency and noise figure. It is shown that the quantum state can be well preserved during the frequency conversion as long as the optical parametric amplifier is operated far below the threshold, and meanwhile injected with an input idler field with a power density about ten times greater than that of the pump. The dependence of the noi…
Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by Josephson ring modulator which acts as a three-wave mixing non-degenerate parametric amplifier. Here, we solve the master equation of three bosonic modes describing the Josephson ring modulator with a novel numerical method to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity…
Josephson parametric amplifiers have emerged as a promising platform for quantum information processing and squeezed quantum states generation. Travelling wave and impedance-matched parametric amplifiers provide broad bandwidth for high-fidelity single-shot readout of multiple qubit superconducting circuits. Here, we present a quantum-limited 3-wave-mixing parametric amplifier based on superconducting nonlinear asymmetric inductive elements (SNAILs), whose useful bandwidth is enhanced with an on-chip two-section impedance-matching circuit based on microstrip transmission lines. The amplifier d…
A Josephson parametric amplifier (JPA) can create squeezed states of microwave light, lowering the noise associated with certain quantum measurements. We experimentally study how the JPA's pump influences the phase-sensitive amplification and deamplification of a coherent tone's amplitude when that amplitude is commensurate with vacuum fluctuations. We predict and demonstrate that by operating the JPA with a pump power greater than the value that maximizes gain, the amplifier distortion is reduced and consequently squeezing is improved. Optimizing the JPA's operation in this fashion, we direct…
We describe a wide-band Josephson Parametric Amplifier (JPA) that is impedance-matched using an integrated compact superconducting transmission line transformer. The impedance transformer consists of two broadside coupled transmission lines configured in a Ruthroff topology which enables a wide matching bandwidth from 2 to 18 GHz, reducing the input line impedance and the device resonance quality factor by a factor of 4. This enables gain flatness and flexibility in the choice of the amplifier's tuning range. The amplifier has up to 20dB gain, with less than 1 dB of ripple, 2-3 GHz gain-bandwi…
Quantum lithography proposes to adopt entangled quantum states in order to increase resolution in interferometry. In the present paper we experimentally demonstrate that the output of a high-gain optical parametric amplifier can be intense yet exhibits quantum features, namely, sub-Rayleigh fringes, as proposed by Agarwal et al. (Phys. Rev. Lett. 86, 1389 (2001)). We investigate multiphoton states generated by a high-gain optical parametric amplifier operating with a quantum vacuum input for a gain values up to 2.5. The visibility has then been increased by means of three-photon absorption. Th…
We discuss the concept of characteristic squeezing modes applied to a travelling-wave optical parametric amplifier pumped by an ultrashort pulse. The characteristic modes undergo decoupled single-mode squeezing transformations, and therefore they form a useful basis to describe the evolution of the entire multimode system. This provides an elegant and intuitive picture of quantum statistical properties of parametric fluorescence. We analyse the efficiency of detecting quadrature squeezing, and present results of numerical calculations for a realistic nonlinear medium.
Squeezed vacuum field can be amplified or deamplified when it is injected, as the signal beam, into a phase-sensitive optical parametric amplifier (OPA) inside an optical cavity. The spectral features of the reflected quantized signal field are controlled by the relative phase between the injected squeezed vacuum field and the pump field for the OPA. The experimental results demonstrate coherent phenomena of OPA in the quantum regime, and show phase-sensitive manipulations of quantum fluctuations for quantum information processing.
The 'Ghost' interference experiment is analyzed when the source of entangled photons is a multimode Optical Parametric Amplifier(OPA) whose weak limit is the two-photon Spontaneous Parametric Downconversion(SPDC) beam. The visibility of the double-slit pattern is calculated, taking the finite coincidence time window of the photon counting detectors into account. It is found that the coincidence window and the bandwidth of light reaching the detectors play a crucial role in the loss of visibility on coincidence detection, not only in the 'Ghost' interference experiment but in all experiments in…
Spin squeezing is one of the most attractive methods for realizing high-precision metrology. In this paper, we propose a protocol for generating spin squeezing in an atomic ensemble via a fully quantum degenerate parametric amplifier. We discuss the properties of generating spin squeezing with and without driving the pump cavity. Numerical simulation results show that the generated spin squeezing strength is sizable, and is able to be comparable to that obtained using a two-axis twisting (TAT) model. Moreover, we demonstrate that the protocol is experimentally feasible by introducing the corre…
We experimentally demonstrated that the quantum correlations of amplitude and phase quadratures between signal and idler beams produced from a non-degenerate optical parametric amplifier (NOPA) can be significantly improved by using a mode cleaner in the pump field and reducing the phase fluctuations in phase locking systems. Based on the two technical improvements the quantum entanglement measured with a two-mode homodyne detector is enhanced from ~ 4 dB to ~ 6 dB below the quantum noise limit using the same NOPA and nonlinear crystal.
We propose a scheme to modulate the entanglement between two oscillators separated in space via the squeezing cavity field generated by the optical parametric amplifier instead of injecting the squeezing field directly with the assistance of Coulomb interaction. We show that the Coulomb interaction between the oscillators is the essential reason for the existence of entanglement. Due to the gain of the optical parametric amplifier and the phase of the pump driving the optical parametric amplifier can simultaneously modulate the squeezing cavity field, the radiation pressure interaction between…
We experimentally demonstrate that the quantum entanglement between amplitude and phase quadratures of optical modes produced from a non-degenerate optical parametric amplifier (NOPA) can be enhanced and manipulated phase-sensitively by means of another NOPA. When both NOPAs operate at de-amplification, the entanglement degree is increased at the cavity resonance of the second NOPA. When the first NOPA operates at de-amplification and the second one at amplification, the spectral features of the correlation variances are significantly changed. The experimental results are in good agreement wit…
We describe the realization of multimode phononic correlations that arise from nonlinear interactions in a mechanical nondegenerate parametric amplifier. The nature of these correlations differs qualitatively depending on the strength of the driving field in relation to the threshold for parametric instability. Below this threshold, the correlations are manifest in a combined quadrature of the coupled mechanical modes. In this regime, the system is amenable to back-action evading measurement schemes for the detection of weak forces. Above threshold, the correlations are manifest in the amplitu…
We study the effect of photothermal fluctuations on squeezed states of light through the photo-refractive effect and thermal expansion in a degenerate optical parametric amplifier (OPA). We also discuss the effect of the photothermal noise in various cases and how to minimize its undesirable consequences. We find that the photothermal noise in the OPA introduces a significant amount of noise on phase squeezed beams, making them less than ideal for low frequency applications such as gravitational wave (GW) interferometers, whereas amplitude squeezed beams are relatively immune to the phototherm…
We propose a scheme for entangling the motional mode of a trapped atom with a propagating light field via a cavity-mediated parametric interaction. We then show that if this light field is subsequently coupled to a second distant atom via a cavity-mediated linear-mixing interaction, it is possible to transfer the entanglement from the light beam to the motional mode of the second atom to create an EPR-type entangled state of the positions and momenta of two distantly-separated atoms.
A Josephson parametric amplifier (JPA) is executed in a three-dimensional (3D) microwave cavity by coupling it to a superconducting quantum interference device (SQUID) that is embedded in a two-dimensional resonator. The JPA is activated in a three-wave mixing configuration by injecting ac magnetic flux, at twice the 3D cavity frequency, into the SQUID. An 8.3 GHz cavity is measured in a non-degenerate phase-insensitive configuration which yields gains in excess of 40 dB, where a 20 dB gain results in an operational bandwidth of 0.4 MHz, a 1 dB compression point of -115 dBm with half a quantum…
We demonstrate quantum correlations in the transverse plane of continuous wave light beams by producing -4.0 dB, -2.6 dB and -1.5 dB of squeezing in the TEM00, TEM10 and TEM20 Hermite- Gauss modes with an optical parametric amplifier, respectively. This has potential applications in quantum information networking, enabling parallel quantum information processing. We describe the setup for the generation of squeezing and analyze the effects of various experimental issues such as mode overlap between pump and seed and nonlinear losses.
We show how the Jaynes--Cummings--Rabi model of cavity quantum electrodynamics can be realized via an isomorphism to the Hamiltonian of a qubit inside a parametric amplifier cavity. This realization clears the way to observe the full spectrum of the Rabi model via a probe applied to a parametric amplifier cavity containing a qubit and a parametric oscillator operating below threshold. An important outcome of the isomorphism is that the actual frequencies are replaced by detunings which make it feasible to reach the ultra-strong coupling regime. We find that inside this regime the probed spectr…
We propose a simple model for the nondegenerate parametric inter- action that takes into account the finite spectral bandwidth of the pump wave. The Heisenberg equations of motion are solved exactly and we show that the bosonic operators obey to a generalized Bogoliubov transforma- tion, where the degree of squeezing depends on the spectral bandwidth. The average number of photons produced in the interaction, the degree of squeezing as well as the degree of entanglement are computed showing that they decrease with increasing spectral bandwidth.
Traditional method for measuring continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses resulted from many factors such as detector's quantum efficiency and mode mismatching between detected field and local oscillator. In this paper, we propose and analyze a new measurement method, which is realized by assisting the balanced homodyne detections with a high gain phase sensitive parametric amplifier. The employment of the high gain parametric amplifier helps to tackle the vacuum quantum noise originat…
We propose a method to enhance bipartite and tripartite entanglement in cavity magnomechanics using an optical parametric amplifier (OPA). We analyze this system and identified parametric regimes where different types of entanglement are enhanced. We show that a proper choice of the phase of the parametric amplifier leads to the enhancement of the bipartite entanglements. Moreover, the tripartite entanglement is also significantly enhanced in the presence of OPA. The OPA not only enhances the strength of entanglement but also increases the domain of entanglement over a wider space of detunings…
We introduce a novel near-quantum-limited amplifier with a large tunable bandwidth and high dynamic range - the Josephson Array Mode Parametric Amplifier (JAMPA). The signal and idler modes involved in the amplification process are realized by the array modes of a chain of 1000 flux tunable, Josephson-junction-based, nonlinear elements. The frequency spacing between array modes is comparable to the flux tunability of the modes, ensuring that any desired frequency can be occupied by a resonant mode, which can further be pumped to produce high gain. We experimentally demonstrate that the device …
Squeezing of the electromagnetic vacuum is an essential metrological technique used to reduce quantum noise in applications spanning gravitational wave detection, biological microscopy, and quantum information science. In superconducting circuits, the resonator-based Josephson-junction parametric amplifiers conventionally used to generate squeezed microwaves are constrained by a narrow bandwidth and low dynamic range. In this work, we develop a dual-pump, broadband Josephson traveling-wave parametric amplifier that combines a phase-sensitive extinction ratio of 56 dB with single-mode squeezing…
Recent experimental results demonstrated the generation of a quantum superpositon (MQS), involving a number of photons in excess of 5x10^4, which showed a high resilience to losses. In order to perform a complete analysis on the effects of de-coherence on this multiphoton fields, obtained through the Quantum Injected Optical Parametric Amplifier (QIOPA), we invesigate theoretically the evolution of the Wigner functions associated to these states in lossy conditions. Recognizing the presence of negative regions in the W-representation as an evidence of non-classicality, we focus our analysis on…
We investigate experimentally the absorptive and dispersive properties of triple-resonant optical parametric amplifier OPA for the degenerate subharmonic field. In the experiment, the subharmonic field is utilized as the probe field and the harmonic wave as the pump field. We demonstrate that EIT-like effect can be simulated in the triple-resonant OPA when the cavity line-width for the harmonic wave is narrower than that for the subharmonic field. However, this phenomenon can not be observed in a double-resonant OPA. The narrow transparency window appears in the reflected field. Especially, in…
High gain parametric amplifier with a single-pass pulsed pump is known to generate broadband twin photon fields that are entangled in amplitude and phase but have complicated spectral correlation. Fortunately, they can be decomposed into independent temporal modes. But the common treatment of parametric interaction Hamiltonian does not consider the issue of time ordering problem of interaction Hamiltonian and thus leads to incorrect conclusion that the mode structure and the temporal mode functions do not change as the gain increases. In this paper, we use an approach that is usually employed …
The linear time-dependent constants of motion of the parametric amplifier are obtained and used to determine in the tomographic-probability representation the evolution of a general two-mode Gaussian state. By means of the discretization of the continuous variable density matrix, the von Neumann and linear entropies are calculated to measure the entanglement properties between the modes of the amplifier. The obtained results for the nonlocal correlations are compared with those associated to a linear map of discretized symplectic Gaussian-state tomogram onto a qubit tomogram. This qubit portra…
We demonstrate that a phase-insensitive parametric amplifier, coupled to a quantum correlated source, can be used as a quantum information tap for noiseless three-way signal splitting. We find that the output signals are amplified noiselessly in two of the three output ports while the other can more or less keep its original input size without adding noise. This scheme is able to cascade and scales up for efficient information distribution in an optical network. Furthermore, we find this scheme satisfies the criteria for a non-ideal quantum non-demolition (QND) measurement and thus can serve a…
One of the central challenges in the development of parametric amplifiers is the control of the dynamic range relative to its gain and bandwidth, which typically limits quantum limited amplification to signals which contain only a few photons per inverse bandwidth. Here, we discuss the control of the dynamic range of Josephson parametric amplifiers by using Josephson junction arrays. We discuss gain, bandwidth, noise, and dynamic range properties of both a transmission line and a lumped element based parametric amplifier. Based on these investigations we derive useful design criteria, which ma…
Non-linearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA), the only device in which the quantum limit has so far been achieved at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) non-linearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type non-linearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction non-linearity in the linear response regim…
We theoretically investigate optical detection of a weak classical force acting on a free particle in a dissipative coupling optomechanical system with a degenerate parametric amplifier (PA). We show that the PA allows one to achieve the force sensitivity far better than the standard quantum limit (SQL) over a broad range of the detection frequencies. The improvement depends on the parametric gain and the driving power. Moreover, we discuss the effects of the mechanical damping and the thermal noise on the force sensitivity. We find that the robustness of the force sensitivity much better than…
Superconducting parametric amplifiers have great promise for quantum-limited readout of superconducting qubits and detectors. Until recently, most superconducting parametric amplifiers had been based on resonant structures, limiting their bandwidth and dynamic range. Broadband traveling-wave parametric amplifiers based both on the nonlinear kinetic inductance of superconducting thin films and on Josephson junctions are in development. By modifying the dispersion property of the amplifier circuit, referred to as dispersion engineering, the gain can be greatly enhanced and the size can be reduce…
